How can I scale a set of vertices to the size of another set of vertices?
In the begining, create shape keys you'll use for animation (as NoviceInDisguise suggested, thanks):



Then, in Edit mode you select the vertices you'd like to scale. To not mess up pivot center, select only vertices located on one plane. Turn on snap during transform with Shift + Tab, set the Pivot Point to the median with Ctrl+&lt;:



In this case you don't need to remove doubles, and now it's possible to use shape key, created before. In Object mode drag the slider and test how it works: